Calculate the Area: Finding Ascending Region of f(x)=6x²-12

Video Solution

Solution Steps

00:00 Find the domain of increase of the function

00:04 Let's examine the trinomial coefficients

00:10 Let's examine the coefficient of X squared, it's positive so the function is happy

00:16 We'll use the formula to find the vertex of the parabola

00:19 We'll substitute appropriate values according to the given data and solve to find the vertex

00:22 This is the X value at the vertex of the parabola

00:30 We'll determine when the parabola is decreasing and when it's increasing based on its type

00:38 We'll draw the X-axis and find the domain of increase

00:41 And this is the solution to the question

Step-by-Step Solution

To determine the ascending area of the function $f(x) = 6x^2 - 12$ , we will follow these steps:

Step 1: Calculate the derivative of the given function.
Step 2: Set the inequality $f'(x) > 0$ to find the interval where the function is increasing.
Step 3: Solve the inequality for $x$ .

Let's begin with Step 1:
The derivative of $f(x) = 6x^2 - 12$ with respect to $x$ is:

$f'(x) = \frac{d}{dx}(6x^2 - 12) = 12x$ .

Step 2: We need to find where $12x > 0$ . This requires:

$x > 0$ .

Step 3: Therefore, the function $f(x) = 6x^2 - 12$ is increasing when $x > 0$ .

Thus, the increasing interval of the function is when $x > 0$ .

The solution to the problem is $0 < x$ .